Question

Solve the following quadratic equation:

2x² + ax – a² = 0

Answer 1

We write, ax = 2ax – ax as 2x² × (–a²) = –2a²x² = 2ax × (–ax) 

∴ 2x² + ax – a² = 0 

⇒ 2x² + 2ax – ax – a² = 0 

⇒ 2x(x + a) – a(x + a) = 0 

⇒ (x + a)(2x – a) = 0 

⇒ x + a = 0 or 2x – a = 0

⇒ `x = -a` or `x = a/2` 

Hence, –a and `a/2` are the roots of the given equation.